it turns out that the problem lay with this roller which was hidden behind the plate at the bottom of the window.
The roller has a spring inside which puts tension on the tape and draws it back in when the shutter is opened. Although the spring seems to be still functioning, it wasn’t doing its job. When we tried to open the shutter, the tape just hung down below.
The simple solution was to replace it with a new one which is what Rafa from Grupo Lorquiva (formerly Pepe Lorente) did yesterday.